// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include <math.h>
#include <memory>
#include <sstream>

#include "main.h"

#include <Eigen/src/Core/arch/Default/BFloat16.h>

#define VERIFY_BFLOAT16_BITS_EQUAL(h, bits)                                                                            \
	VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))

// Make sure it's possible to forward declare Eigen::bfloat16
namespace Eigen {
struct bfloat16;
}

using Eigen::bfloat16;

float
BinaryToFloat(uint32_t sign, uint32_t exponent, uint32_t high_mantissa, uint32_t low_mantissa)
{
	float dest;
	uint32_t src = (sign << 31) + (exponent << 23) + (high_mantissa << 16) + low_mantissa;
	memcpy(static_cast<void*>(&dest), static_cast<const void*>(&src), sizeof(dest));
	return dest;
}

template<typename T>
void
test_roundtrip()
{
	// Representable T round trip via bfloat16
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(-std::numeric_limits<T>::infinity()))),
					-std::numeric_limits<T>::infinity());
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(std::numeric_limits<T>::infinity()))),
					std::numeric_limits<T>::infinity());
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(T(-1.0)))), T(-1.0));
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(T(-0.5)))), T(-0.5));
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(T(-0.0)))), T(-0.0));
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(T(1.0)))), T(1.0));
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(T(0.5)))), T(0.5));
	VERIFY_IS_EQUAL((internal::cast<bfloat16, T>(internal::cast<T, bfloat16>(T(0.0)))), T(0.0));
}

void
test_conversion()
{
	using Eigen::bfloat16_impl::__bfloat16_raw;

	// Round-trip casts
	VERIFY_IS_EQUAL(numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(1.0f))), bfloat16(1.0f));
	VERIFY_IS_EQUAL(numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.5f))), bfloat16(0.5f));
	VERIFY_IS_EQUAL(numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(-0.33333f))),
					bfloat16(-0.33333f));
	VERIFY_IS_EQUAL(numext::bit_cast<bfloat16>(numext::bit_cast<numext::uint16_t>(bfloat16(0.0f))), bfloat16(0.0f));

	// Conversion from float.
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1.0f), 0x3f80);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f), 0x3f00);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.33333f), 0x3eab);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.38e38f), 0x7f7e);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3.40e38f), 0x7f80); // Becomes infinity.

	// Verify round-to-nearest-even behavior.
	float val1 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c00)));
	float val2 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c01)));
	float val3 = static_cast<float>(bfloat16(__bfloat16_raw(0x3c02)));
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val1 + val2)), 0x3c00);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.5f * (val2 + val3)), 0x3c02);

	// Conversion from int.
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-1), 0xbf80);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0), 0x0000);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(1), 0x3f80);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(2), 0x4000);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(3), 0x4040);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(12), 0x4140);

	// Conversion from bool.
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(false), 0x0000);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(true), 0x3f80);

	// Conversion to bool
	VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(3)), true);
	VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.33333f)), true);
	VERIFY_IS_EQUAL(bfloat16(-0.0), false);
	VERIFY_IS_EQUAL(static_cast<bool>(bfloat16(0.0)), false);

	// Explicit conversion to float.
	VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x0000))), 0.0f);
	VERIFY_IS_EQUAL(static_cast<float>(bfloat16(__bfloat16_raw(0x3f80))), 1.0f);

	// Implicit conversion to float
	VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x0000)), 0.0f);
	VERIFY_IS_EQUAL(bfloat16(__bfloat16_raw(0x3f80)), 1.0f);

	// Zero representations
	VERIFY_IS_EQUAL(bfloat16(0.0f), bfloat16(0.0f));
	VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(0.0f));
	VERIFY_IS_EQUAL(bfloat16(-0.0f), bfloat16(-0.0f));
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(0.0f), 0x0000);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(-0.0f), 0x8000);

	// Default is zero
	VERIFY_IS_EQUAL(static_cast<float>(bfloat16()), 0.0f);

	// Representable floats round trip via bfloat16
	test_roundtrip<float>();
	test_roundtrip<double>();
	test_roundtrip<std::complex<float>>();
	test_roundtrip<std::complex<double>>();

	// Conversion
	Array<float, 1, 100> a;
	for (int i = 0; i < 100; i++)
		a(i) = i + 1.25;
	Array<bfloat16, 1, 100> b = a.cast<bfloat16>();
	Array<float, 1, 100> c = b.cast<float>();
	for (int i = 0; i < 100; ++i) {
		VERIFY_LE(numext::abs(c(i) - a(i)), a(i) / 128);
	}

	// Epsilon
	VERIFY_LE(1.0f, static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() + bfloat16(1.0f)));
	VERIFY_IS_EQUAL(1.0f,
					static_cast<float>((std::numeric_limits<bfloat16>::epsilon)() / bfloat16(2.0f) + bfloat16(1.0f)));

	// Negate
	VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(3.0f)), -3.0f);
	VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4.5f)), 4.5f);

#if !EIGEN_COMP_MSVC
	// Visual Studio errors out on divisions by 0
	VERIFY((numext::isnan)(static_cast<float>(bfloat16(0.0 / 0.0))));
	VERIFY((numext::isinf)(static_cast<float>(bfloat16(1.0 / 0.0))));
	VERIFY((numext::isinf)(static_cast<float>(bfloat16(-1.0 / 0.0))));

	// Visual Studio errors out on divisions by 0
	VERIFY((numext::isnan)(bfloat16(0.0 / 0.0)));
	VERIFY((numext::isinf)(bfloat16(1.0 / 0.0)));
	VERIFY((numext::isinf)(bfloat16(-1.0 / 0.0)));
#endif

	// NaNs and infinities.
	VERIFY(!(numext::isinf)(static_cast<float>(bfloat16(3.38e38f)))); // Largest finite number.
	VERIFY(!(numext::isnan)(static_cast<float>(bfloat16(0.0f))));
	VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0xff80)))));
	VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0xffc0)))));
	VERIFY((numext::isinf)(static_cast<float>(bfloat16(__bfloat16_raw(0x7f80)))));
	VERIFY((numext::isnan)(static_cast<float>(bfloat16(__bfloat16_raw(0x7fc0)))));

	// Exactly same checks as above, just directly on the bfloat16 representation.
	VERIFY(!(numext::isinf)(bfloat16(__bfloat16_raw(0x7bff))));
	VERIFY(!(numext::isnan)(bfloat16(__bfloat16_raw(0x0000))));
	VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0xff80))));
	VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0xffc0))));
	VERIFY((numext::isinf)(bfloat16(__bfloat16_raw(0x7f80))));
	VERIFY((numext::isnan)(bfloat16(__bfloat16_raw(0x7fc0))));

	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x0, 0xff, 0x40, 0x0)), 0x7fc0);
	VERIFY_BFLOAT16_BITS_EQUAL(bfloat16(BinaryToFloat(0x1, 0xff, 0x40, 0x0)), 0xffc0);
}

void
test_numtraits()
{
	std::cout << "epsilon       = " << NumTraits<bfloat16>::epsilon() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::epsilon()) << ")" << std::endl;
	std::cout << "highest       = " << NumTraits<bfloat16>::highest() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::highest()) << ")" << std::endl;
	std::cout << "lowest        = " << NumTraits<bfloat16>::lowest() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::lowest()) << ")" << std::endl;
	std::cout << "min           = " << (std::numeric_limits<bfloat16>::min)() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::min)()) << ")" << std::endl;
	std::cout << "denorm min    = " << (std::numeric_limits<bfloat16>::denorm_min)() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>((std::numeric_limits<bfloat16>::denorm_min)()) << ")" << std::endl;
	std::cout << "infinity      = " << NumTraits<bfloat16>::infinity() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::infinity()) << ")" << std::endl;
	std::cout << "quiet nan     = " << NumTraits<bfloat16>::quiet_NaN() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>(NumTraits<bfloat16>::quiet_NaN()) << ")" << std::endl;
	std::cout << "signaling nan = " << std::numeric_limits<bfloat16>::signaling_NaN() << "  (0x" << std::hex
			  << numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) << ")" << std::endl;

	VERIFY(NumTraits<bfloat16>::IsSigned);

	VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::infinity()),
					numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::infinity())));
	// There is no guarantee that casting a 32-bit NaN to bfloat16 has a precise
	// bit pattern.  We test that it is in fact a NaN, then test the signaling
	// bit (msb of significand is 1 for quiet, 0 for signaling).
	const numext::uint16_t BFLOAT16_QUIET_BIT = 0x0040;
	VERIFY(
		(numext::isnan)(std::numeric_limits<bfloat16>::quiet_NaN()) &&
		(numext::isnan)(bfloat16(std::numeric_limits<float>::quiet_NaN())) &&
		((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::quiet_NaN()) & BFLOAT16_QUIET_BIT) > 0) &&
		((numext::bit_cast<numext::uint16_t>(bfloat16(std::numeric_limits<float>::quiet_NaN())) & BFLOAT16_QUIET_BIT) >
		 0));
	// After a cast to bfloat16, a signaling NaN may become non-signaling. Thus,
	// we check that both are NaN, and that only the `numeric_limits` version is
	// signaling.
	VERIFY((numext::isnan)(std::numeric_limits<bfloat16>::signaling_NaN()) &&
		   (numext::isnan)(bfloat16(std::numeric_limits<float>::signaling_NaN())) &&
		   ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<bfloat16>::signaling_NaN()) & BFLOAT16_QUIET_BIT) ==
			0));

	VERIFY((std::numeric_limits<bfloat16>::min)() > bfloat16(0.f));
	VERIFY((std::numeric_limits<bfloat16>::denorm_min)() > bfloat16(0.f));
	VERIFY_IS_EQUAL((std::numeric_limits<bfloat16>::denorm_min)() / bfloat16(2), bfloat16(0.f));
}

void
test_arithmetic()
{
	VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(2)), 4);
	VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2) + bfloat16(-2)), 0);
	VERIFY_IS_APPROX(static_cast<float>(bfloat16(0.33333f) + bfloat16(0.66667f)), 1.0f);
	VERIFY_IS_EQUAL(static_cast<float>(bfloat16(2.0f) * bfloat16(-5.5f)), -11.0f);
	VERIFY_IS_APPROX(static_cast<float>(bfloat16(1.0f) / bfloat16(3.0f)), 0.3339f);
	VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(4096.0f)), -4096.0f);
	VERIFY_IS_EQUAL(static_cast<float>(-bfloat16(-4096.0f)), 4096.0f);
}

void
test_comparison()
{
	VERIFY(bfloat16(1.0f) > bfloat16(0.5f));
	VERIFY(bfloat16(0.5f) < bfloat16(1.0f));
	VERIFY(!(bfloat16(1.0f) < bfloat16(0.5f)));
	VERIFY(!(bfloat16(0.5f) > bfloat16(1.0f)));

	VERIFY(!(bfloat16(4.0f) > bfloat16(4.0f)));
	VERIFY(!(bfloat16(4.0f) < bfloat16(4.0f)));

	VERIFY(!(bfloat16(0.0f) < bfloat16(-0.0f)));
	VERIFY(!(bfloat16(-0.0f) < bfloat16(0.0f)));
	VERIFY(!(bfloat16(0.0f) > bfloat16(-0.0f)));
	VERIFY(!(bfloat16(-0.0f) > bfloat16(0.0f)));

	VERIFY(bfloat16(0.2f) > bfloat16(-1.0f));
	VERIFY(bfloat16(-1.0f) < bfloat16(0.2f));
	VERIFY(bfloat16(-16.0f) < bfloat16(-15.0f));

	VERIFY(bfloat16(1.0f) == bfloat16(1.0f));
	VERIFY(bfloat16(1.0f) != bfloat16(2.0f));

	// Comparisons with NaNs and infinities.
#if !EIGEN_COMP_MSVC
	// Visual Studio errors out on divisions by 0
	VERIFY(!(bfloat16(0.0 / 0.0) == bfloat16(0.0 / 0.0)));
	VERIFY(bfloat16(0.0 / 0.0) != bfloat16(0.0 / 0.0));

	VERIFY(!(bfloat16(1.0) == bfloat16(0.0 / 0.0)));
	VERIFY(!(bfloat16(1.0) < bfloat16(0.0 / 0.0)));
	VERIFY(!(bfloat16(1.0) > bfloat16(0.0 / 0.0)));
	VERIFY(bfloat16(1.0) != bfloat16(0.0 / 0.0));

	VERIFY(bfloat16(1.0) < bfloat16(1.0 / 0.0));
	VERIFY(bfloat16(1.0) > bfloat16(-1.0 / 0.0));
#endif
}

void
test_basic_functions()
{
	VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(3.5f))), 3.5f);
	VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(3.5f))), 3.5f);
	VERIFY_IS_EQUAL(static_cast<float>(numext::abs(bfloat16(-3.5f))), 3.5f);
	VERIFY_IS_EQUAL(static_cast<float>(abs(bfloat16(-3.5f))), 3.5f);

	VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(3.5f))), 3.0f);
	VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(3.5f))), 3.0f);
	VERIFY_IS_EQUAL(static_cast<float>(numext::floor(bfloat16(-3.5f))), -4.0f);
	VERIFY_IS_EQUAL(static_cast<float>(floor(bfloat16(-3.5f))), -4.0f);

	VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(3.5f))), 4.0f);
	VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(3.5f))), 4.0f);
	VERIFY_IS_EQUAL(static_cast<float>(numext::ceil(bfloat16(-3.5f))), -3.0f);
	VERIFY_IS_EQUAL(static_cast<float>(ceil(bfloat16(-3.5f))), -3.0f);

	VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(0.0f))), 0.0f);
	VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(0.0f))), 0.0f);
	VERIFY_IS_APPROX(static_cast<float>(numext::sqrt(bfloat16(4.0f))), 2.0f);
	VERIFY_IS_APPROX(static_cast<float>(sqrt(bfloat16(4.0f))), 2.0f);

	VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f);
	VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(0.0f), bfloat16(1.0f))), 0.0f);
	VERIFY_IS_APPROX(static_cast<float>(numext::pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f);
	VERIFY_IS_APPROX(static_cast<float>(pow(bfloat16(2.0f), bfloat16(2.0f))), 4.0f);

	VERIFY_IS_EQUAL(static_cast<float>(numext::exp(bfloat16(0.0f))), 1.0f);
	VERIFY_IS_EQUAL(static_cast<float>(exp(bfloat16(0.0f))), 1.0f);
	VERIFY_IS_APPROX(static_cast<float>(numext::exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI));
	VERIFY_IS_APPROX(static_cast<float>(exp(bfloat16(EIGEN_PI))), 20.f + static_cast<float>(EIGEN_PI));

	VERIFY_IS_EQUAL(static_cast<float>(numext::expm1(bfloat16(0.0f))), 0.0f);
	VERIFY_IS_EQUAL(static_cast<float>(expm1(bfloat16(0.0f))), 0.0f);
	VERIFY_IS_APPROX(static_cast<float>(numext::expm1(bfloat16(2.0f))), 6.375f);
	VERIFY_IS_APPROX(static_cast<float>(expm1(bfloat16(2.0f))), 6.375f);

	VERIFY_IS_EQUAL(static_cast<float>(numext::log(bfloat16(1.0f))), 0.0f);
	VERIFY_IS_EQUAL(static_cast<float>(log(bfloat16(1.0f))), 0.0f);
	VERIFY_IS_APPROX(static_cast<float>(numext::log(bfloat16(10.0f))), 2.296875f);
	VERIFY_IS_APPROX(static_cast<float>(log(bfloat16(10.0f))), 2.296875f);

	VERIFY_IS_EQUAL(static_cast<float>(numext::log1p(bfloat16(0.0f))), 0.0f);
	VERIFY_IS_EQUAL(static_cast<float>(log1p(bfloat16(0.0f))), 0.0f);
	VERIFY_IS_APPROX(static_cast<float>(numext::log1p(bfloat16(10.0f))), 2.390625f);
	VERIFY_IS_APPROX(static_cast<float>(log1p(bfloat16(10.0f))), 2.390625f);
}

void
test_trigonometric_functions()
{
	VERIFY_IS_APPROX(numext::cos(bfloat16(0.0f)), bfloat16(cosf(0.0f)));
	VERIFY_IS_APPROX(cos(bfloat16(0.0f)), bfloat16(cosf(0.0f)));
	VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI)), bfloat16(cosf(EIGEN_PI)));
	// VERIFY_IS_APPROX(numext::cos(bfloat16(EIGEN_PI/2)), bfloat16(cosf(EIGEN_PI/2)));
	// VERIFY_IS_APPROX(numext::cos(bfloat16(3*EIGEN_PI/2)), bfloat16(cosf(3*EIGEN_PI/2)));
	VERIFY_IS_APPROX(numext::cos(bfloat16(3.5f)), bfloat16(cosf(3.5f)));

	VERIFY_IS_APPROX(numext::sin(bfloat16(0.0f)), bfloat16(sinf(0.0f)));
	VERIFY_IS_APPROX(sin(bfloat16(0.0f)), bfloat16(sinf(0.0f)));
	// VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI)), bfloat16(sinf(EIGEN_PI)));
	VERIFY_IS_APPROX(numext::sin(bfloat16(EIGEN_PI / 2)), bfloat16(sinf(EIGEN_PI / 2)));
	VERIFY_IS_APPROX(numext::sin(bfloat16(3 * EIGEN_PI / 2)), bfloat16(sinf(3 * EIGEN_PI / 2)));
	VERIFY_IS_APPROX(numext::sin(bfloat16(3.5f)), bfloat16(sinf(3.5f)));

	VERIFY_IS_APPROX(numext::tan(bfloat16(0.0f)), bfloat16(tanf(0.0f)));
	VERIFY_IS_APPROX(tan(bfloat16(0.0f)), bfloat16(tanf(0.0f)));
	// VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI)), bfloat16(tanf(EIGEN_PI)));
	// VERIFY_IS_APPROX(numext::tan(bfloat16(EIGEN_PI/2)), bfloat16(tanf(EIGEN_PI/2)));
	// VERIFY_IS_APPROX(numext::tan(bfloat16(3*EIGEN_PI/2)), bfloat16(tanf(3*EIGEN_PI/2)));
	VERIFY_IS_APPROX(numext::tan(bfloat16(3.5f)), bfloat16(tanf(3.5f)));
}

void
test_array()
{
	typedef Array<bfloat16, 1, Dynamic> ArrayXh;
	Index size = internal::random<Index>(1, 10);
	Index i = internal::random<Index>(0, size - 1);
	ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
	VERIFY_IS_APPROX(a1 + a1, bfloat16(2) * a1);
	VERIFY((a1.abs() >= bfloat16(0)).all());
	VERIFY_IS_APPROX((a1 * a1).sqrt(), a1.abs());

	VERIFY(((a1.min)(a2) <= (a1.max)(a2)).all());
	a1(i) = bfloat16(-10.);
	VERIFY_IS_EQUAL(a1.minCoeff(), bfloat16(-10.));
	a1(i) = bfloat16(10.);
	VERIFY_IS_EQUAL(a1.maxCoeff(), bfloat16(10.));

	std::stringstream ss;
	ss << a1;
}

void
test_product()
{
	typedef Matrix<bfloat16, Dynamic, Dynamic> MatrixXh;
	Index rows = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
	Index cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
	Index depth = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
	MatrixXh Ah = MatrixXh::Random(rows, depth);
	MatrixXh Bh = MatrixXh::Random(depth, cols);
	MatrixXh Ch = MatrixXh::Random(rows, cols);
	MatrixXf Af = Ah.cast<float>();
	MatrixXf Bf = Bh.cast<float>();
	MatrixXf Cf = Ch.cast<float>();
	VERIFY_IS_APPROX(Ch.noalias() += Ah * Bh, (Cf.noalias() += Af * Bf).cast<bfloat16>());
}

EIGEN_DECLARE_TEST(bfloat16_float)
{
	CALL_SUBTEST(test_numtraits());
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST(test_conversion());
		CALL_SUBTEST(test_arithmetic());
		CALL_SUBTEST(test_comparison());
		CALL_SUBTEST(test_basic_functions());
		CALL_SUBTEST(test_trigonometric_functions());
		CALL_SUBTEST(test_array());
		CALL_SUBTEST(test_product());
	}
}
